(x +3)3 4(x – 1)2 12 16 Consider the function f(x) 11 Note that (x – 1)2 4 1 - - (x – 9)(x+ 3)² 24(r + 3) f'(x) = and f"(x) = 4(x – 1)3 (r – 1)ª Use the Mean Value Theorem to show that the equation f'(x) = 0.01 has a solution in the interval (-4,-3)

Q: 8. Find f'(x) for the function f (x) = (5x² + 3)4

A: ddxfxn=nfxn-1f'x

Q: Consider the following table xf(x)g(x)f'(x)g'(x) 02 5 0 2 11 -2 3 24 4 1 -1 33 -3 2 3 What is h'(2)…

A:

Q: Find f(") (x) given f (x) = In(x + 1)

A: Given function is  f(x) = ln(x+1)  We have to find the nth derivative of f i.e. fn. We use  notation…

Q: Suppose that f is a function with f'(2) = −5. If u is very very close to 0, then f(2 + u) is…

A:

Q: 8 If f(t) = 13t5 and f(t) is the derivative of a function F(t), then F) could be 8 (A) 5t5 +1 8. (B)…

A:

Q: Find the general form of f if f'(x) = 5f(x).

A:

Q: Consider the function h(z), for which h(4) = -12 and h'(4) = -7. %3D h(z) Find f'(4) for the…

A: To Determine: find f'4 Given: consider the function h(x) for which h4=-12 and h'4=-7 also…

Q: 1. Determine f'(x) for each function below: f(x) = x2 – 2x + 3 f(x) = 7x3 · Vx %3D f(x) = x³ In x…

A: As per our company guidelines we are supposed to answer only first three sub-parts. Kindly repost…

Q: Let f(x) = In[x4(x +9)6(x2 + 4)3]. Find f'(x). f'(x) =

A: Given,

Q: Si s(2x)dx = 23. If f is a continuous fiunction and if F'(x) = ƒ(x) for all real numbers x, then (A)…

A:

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: If f be the function defined by f (x) = x³ + x. lf g (x) = f−¹ (x) and g (2) = 1, what is the value…

A:

Q: 4. Let f'(x) = 2ax³ + 3bx² - 6ax+b such that f(x) is concave up on the interval -1 <x< 1 and concava…

A:

Q: (vii) If f(1) = 10 and f'(x) > 2 for 1 < x < 4, how small can f(4) possibly be? Give proper…

A:

Q: Cet f(x): f'(12) = 4x - 3 5x67 Evaluate f'(x) at x = 12.

A: f(x)=4x-35x-6d dx(ab)=bd dx(a)-ad dx(b)b2d dx(xn)=nxn-1

Q: If f(x) = (3x – 2)(2x + 3), then a. f(– 2) b. f'( – 2) = c. f''(– 2) d. The values of x for which…

A:

Q: 2. f(x) f(0) S() 0 f(0) f x) 0I=

A: First we  find equation of line that is  y= mx+b Here m=-2 and b = 2 So equation form and it is y=…

Q: Suppose f(x) and g(x) are two functions such that: • f(3)=1 • g(3)=1 • f(3)=5 • g'(3)=7 What is…

A: we know that uv' = u'v+v'u                   product chain rule of differentiation

Q: Let P(x) = F(x)G(x) and Q(x) = F(x) where F and G are the functions whose grap G(x) y F 2 -1 4 8.…

A: