Given that f(x)x) h(-1) 3 Calculate f(-1) [HINT: Use the product rule and the power rule.]

Q: 9. Let f(x) = xr – 3x² + 3.

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Q: Evaluate f''(c) at the point. f(x) = (x2 - 4)(x3- 2), c = 1

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Q: 4. Let f(x)=1+x³-x. Find an x-value that makes f(x) 0.

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Q: If f(x) = 1 4x - 1 384 (4x-1) 24 (4x - 1)¹ 24 (4x - 1)4 384 (4x - 1)¹ -, then what is f"" (x)?

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Q: Let h(x)=f(x)−g(x). If f(x)=9x^2 and g(x)=8x, what is h′(−5)?

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Q: Let h(x)=f(x)g(x) where f(x)=−4x^2−5x+1, g(1)=−5, and g′(1)=−4 what is h′(1)?

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Q: Find a formula for f-'(x) and (f -1)'(x) if f(x) = V х-2

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Q: Let h(x)=f(x)g(x). If f(x)=x2−3x,g(0)=−1, and g′(0)=−4, what is h′(0)?

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Q: Given that f(x) =x+4 and g(x)=x -x, find (f+g)(1), if it exists. -X,

A: Given two functions f(x) and g(x). Then (f+g)(x)=f(x)+g(x)

Q: (c) Show that f(x)>0 for all values of x, x # -2.

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Q: 3.4 Differentiate f(x) = a°x* - 5ax with respect to x. Assume that a is a constant. f'(x) =D

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Q: 6. Sketch f(x) and it's reciprocal f (x) = -2x -4 %3D %3D

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Q: If you need to prove that a ∈ f^−1 (Y ), what do you need to show?

A: Here we need to show the way to prove a∈f-1(Y)

Q: If f(x) is a differentiable function such that f'(-2)=-1 and g(x)=f(3x+1), then what is g'(-1)?

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Q: 1. Use the limit definition of the derivative to find g'(x) if g(x) = 2x² – 6x + 13.

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Q: a. Differentiate f (x) = x²lnx with respect to x b. Proof that f" (2x + 4xlnx)dx = 2e2

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Q: Let k(x)=f(x)g(x)h(x). If f(x)=−3x+4,g(x)=−x+4, and h(x)=−3x2−4x+3, what is k′(x)?

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Q: 2 For the function f(x) = -x', find f'"(x), f'"(0), f'"(1), and f"(- 1).

A: To find the double derivative for the given function.

Q: Let h(x) where f(x) = In(3x² + 2x + 2) and g(x) = -2x. What is h'(x)?

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Q: Let k(x)=f(x)g(x)h(x). If f(x)=−2x−3,g(x)=−3x+3, and h(x)=−3x2+x+1, what is k′(1)?

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Q: Let k(x)=f(x)g(x)h(x). If f(x)=3x−2,g(x)=2x−3, and h(x)=−2x2+4x, what is k′(1)?

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Q: What are the critical points for the function f(x) = x³ + 6x² – 36x + 7. %3D

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Q: - Given the function f(x) below, evaluate f(-3). 7x 2 if x 0

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Q: Let h(x)=f(x)g(x). If f(x)=4x^2+3x+1 and g(x)=3x^2−3x−4, what is h′(−1)?

A: Given: hx=fxgx, fx=4x2+3x+1, gx=3x2-3x-4

Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

Q: let h(x) = f(x)/g(x), where f(x) = -3x^2 + 2x + 2 and g(x) = -2, what is h'(x)?

A: Given  hx=fxgxwherefx=-3x2+2x+2gx=-2 To find the derivative of h(x) Quotient rule is to be used…

Q: Find f(-3), given x-2 げrs -1 f(x)3D| 3x+1 げェ>-1)

A: We need to find out f(-3) here x=-3 that means x≤-1.

Q: Evaluate f"(c) at the point. 9) f(x) = In (4x - 3), c = 1 10) f(x)=3x2-3, c=1 3x - 4 11) f(x)= 4x-3'…

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Q: 2. If f"(x) = 4sinx+16cosx, f(0) = 6, f'(0) = 1, find f(x) and f(4).

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Q: Let f(x) (x- 2)3. a. Does f'(2) exist? b. Show that the only local extreme value of f occurs at x 2…

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Q: Compute f '(a) algebraically for the given value of a. (x) = x2 - 8; a = 9 f '(a)

A: Given : f(x) = x2-8

Q: (e2* ) In(3x+2) Vx' - x -1 Determine f '(x) if f(x)= DO NOT SIMPLIFY!

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Q: Let h(x)=f(x)g(x). If f(x)=−3x2+2x−3 and g(x)=−3x2+4x+3, what is h′(1)?

A: Given:h(x)-f(x)g(x)f(x)=-3x2+2x-3g(x)=-3x2+4x+3

Q: Use the Intermediate Value Theorem to show 11. f(x)=2x' +3x-1 has a zero between a = 0 and b = 1.

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Q: Given that f(x) = h(x) x5 f'(-1). Show your work. -, h(-1) = 4, and h' (-1) = 7 find

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Q: f(c) {}} [=+3 = < (3x + 1

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Q: Find the are under the graph of f(x) = 4-x2  on the interval (-2,1)

A: Given, f(x) =4-x2  we have to find the area under the curve on the interval (-2,1)

Q: Let h(x) = f(x)g(x). If f (x) = 3x² – x – 4 and g(x) = -x² + 2, what is h' (-1)?

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Q: If f(x) = x² find a ō such that 0 < lx - 21 < & implies 1x² - 41 < F when = 1.

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Q: i) find f (x) given that f(x) = X-2 2x+1) k) Differentiate y= (2x+1 (x-x 1), get your answer in…

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Q: 8. For the function f(x)=3x+5-11, find the values of x such that f(x)=0.

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Q: f(x) = x* – }x' – x + 2x –1 -

A: Given   f(x)= 14x4-23x3-12x2+2x-1has turning point at where the f'(x)=0differntiate f(x) with…

Q: Let f(x) = x2 – 6 and po = 3 and pi = 2. Use Secant method Example: to find p3.

A: Given: f(x)=x2-6, p0=3 and p1=2 To find: Value of p3 using Secant method.

Q: Let h(x)=f(x)g(x). If f(x)=2x2+1,g(1)=0, and g′(1)=−1, what is h′(1)?

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Q: Develop a general rule for f(n)(x) given f (x).…

A: the function given to us is    f(x) = xn

Q: Let h(x)=f(x)/g(x) where f(x)=x^2+5x−1, g(2)=−4, and g′(2)=−2 what is h′(2)?

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Q: If F(x) is an antiderivative of x2 + x1, then what is the value of F(1) - F(-1)? -2

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Q: Let h(x)=f(x)g(x) where f(x)=2x^2−4x, g(−2)=4, and g′(−2)=−5 what is h′(−2)?

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Q: .If f (x) = 5x - 2, g (x) = 2x - 3 and h (x) = x2, then (fogoh) (-1) =

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Q: Given that f(x) = x°h(x) h( – 1) = 5 h'(-1) = 8 Calculate f'(- 1). Hint: Use the product rule and…

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