# interval notation

10:01 Done answer_22 Find (f.n(x). ze Find the domain of (f. n(x). (Enter your answer using interval notation.) مه رمه) () Find (g. g)(x). x + 18 Find the domain of (g. g)(x). (Enter your answer using interval notation.) ره) c- Need Help? Read it Watch It Master it 3. (-/1 Points) DETAILS SCALCET8 3.4.053. MY NOTES ASK YOUR TEACHER Find an equation of the tangent line to the curve at the given point. y = sin(sin(x)), (47,0) ܒ 4 ñ-x 4. (-/1 Points) DETAILS SCALCET8 3.4.063. MY NOTES ASK YOUR TEACHER A table of values for f, g, f’, and g’ is given. х f(x) g(x) f'(x) g'(x) 1 3 2 4 6 2. 8 5 7 1 7 3 2. 7 9 g (f(z)). f'(2) (a) If h(x) = f(g(x)), find h'(1). h'(1) = (b) If H(x) = g(f(x)), find H'(2). H'(2) = 30 4. [-12 Points] DETAILS SCALCET8 3.3.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find an equation of the tangent line to the curve at the given point. y = 7e* cos(x), (0,7) y = 7x +7 Need Help? Read it 5. [2/2 Points) DETAILS PREVIOUS ANSWERS SCALCET8 3.3.028. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER If f(x) = 3e* cos(x), find f ‘(x) and f “(x). -3e’sin(x) + 3e cos(x) f “(x) = -6e’sin(x) Need Help? Read It 3. (-/1 Points) DETAILS SCALCET8 3.4.053. MY NOTES ASK YOUR TEACHER Find an equation of the tangent line to the curve at the given point. y = sin(sin(x)), (44, 0) y = 47-X 4. (-/1 Points) DETAILS SCALCET8 3.4.063. MY NOTES ASK YOUR TEACHER A table of values for f, g, f’, and g’ is given. х f(x) g(x) f'(x) g'(x) 1 3 2 4 6 2. 1 8 5 7 3 7 2 7 9 g'(FC2)).FC2) (a) If h(x) = f(g(x)), find h'(1). h'(1) = (b) If H(x) = g(f(x)), find H'(2). H'(2) = 30 3. [-/1 Points] DETAILS SCALCET8 3.2.031. MY NOTES ASK YOUR TEACHER Find an equation of the tangent line to the given curve at the specified point. x²1 y = (1,0) x2 + x + 1 x- y = تواس 4. (-/1 Points] DETAILS SCALCET8 3.2.050. MY NOTES ASK YOUR TEACHER Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F and Gare the functions whose graphs are shown. 3 3 F ta © 12 12 G – 1 (#) -5(-3 2 이 1라 (a) Find P ‘(2). 3 Ź + 10 my alt (b) Find Q'(7) 4 6. [-/1 Points] DETAILS SCALCET8 3.1.AE.008. MY NOTES ASK YOUR TEACHER If f(x) = ex – x, find f’ and f”. Compare the graphs of f EXAMPLE 8 and fl. SOLUTION Using the Difference Rule, we have f f'(x) = (ex – dx x) = (*) – ਰੰਕ (*) = -1.5 1.5 In an earlier section we defined the second derivative as the derivative of f’, SO f'(x) = (ex – 1) = dx le) – (1) = dx dx Video Example) The function f and its derivative f’ are graphed in the figure to the left. Notice that f has a horizontal tangent when x = ; this corresponds to the fact that f(0) = Notice also that, for x > 0, f'(x) is —Select– and f is –Select— When x < 0, f'(x) is —Select— V and is —Select— Need Help? Read It Submit Answer ^ V Done —Select— positive negative 2. (-/1 Points] DETAILS SCALCET8 3.9.006. MY NOTES ASK YOUR TEACHER The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the diameter is 100 mm? mm3/s 500oT du 45 (50) 5 at 3. (-/1 Points) DETAILS SCALCET8 3.9.014. MY NOTES ASK YOUR TEACHER If a snowball melts so that its surface area decreases at a rate of 6 cm2/min, find the rate at which the diameter decreases when the diameter is 8 cm. 3 A=4r cm/min Ta 8 T 6 at (8) 2 3. (-12 points) DETAILS SCALCET8 3.9.014. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER If a snowball melts so that its surface area decreases at a rate of 9 cm2/min, find the rate at which the diameter decreases when the diameter is 12 cm. cm/min – 3 81 Need Help? Read it 8. (-12 points) DETAILS SCALCET8 3.9.037.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Boyle’s Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 200 cm3, the pressure is 80 kPa, and the pressure is increasing at a rate of 10 kPa/min. At what rate is the volume decreasing at this instant? cm3/min 25 Need Help? Read It Watch It Master it 9. (-12 points) DETAILS SCALCET8 3.10.003. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the linearization L(x) of the function at a. f(x) = Vx. a = 4 L(x) = 1 x tl 4 Need Help? Read it Watch It 10. [-12 Points] DETAILS SCALCET8 3.10.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find the differential of each function. (a) y =tan(70) (G Sec 7t tan it at dy = (b) y = 1 – 2 1 + 2 du dy = -4V (tu) Need Help? Read It Watch It 7. (-12 points) DETAILS SCALCET8 3.11.040. MY NOTES ASK YOUR TEACHER Find the derivative. y = sinh- (tan(x)) y'(x) = secx tan x tl Need Help? Read it 3. [0.5/1 Points] DETAILS PREVIOUS ANSWERS SCALCET8 3.10 (a) Find the differential dy. y = eX/4 ( 🙂 dy = e •dx 4 (b) Evaluate dy for the given values of x and dx. x = 0, dx = 0.01 dy = 0.025 X 3. [0/2 Points] DETAILS PREVIOUS ANSWERS SCALCET8 3.9.014. If a snowball melts so that its surface area decreases at a rate of 9 cm²/min, find the rate at which the diameter decreases when the diameter is 12 cm, 3 cm/min 41 X Enhanced Feedback Please try again. Keep in mind that the surface area of a snowball (sphere) with radius r is A = 470/2. Differentiate this equation with respect to time, t, using the Chain R from the exercise to evaluate the rate of change of the radius of the sphere. Have in mind that the diameter is twice the radius. Need Help? Read it 10. [1/2 Points] DETAILS PREVIOUS ANSWERS SCALCET8 3.10.013. Find the differential of each function. (a) y = tan(70) ( ) dy = V 7 sec? Vot = x (b) 1 – 12 = 1 + 12 12v -47 dy = dv (1 + 2)2″ Need Help? Readi! Watch it

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