30. Find F'(2) given that f(2) 1. f'(2) 4, g(2) = 1 and g'(2) = - 5 a) F(r) = 5/(r) + 29(r) b) F(1) = f(r)g(r) c) F(x) = f(r)/g(r)

Q: Find f. f"(x) = −4+ 8x - 12x², f(0) = 4, f'(0) = 12 (Prob. 1,

A: Consider the derivative function and initial conditions, f''x=-4+8x-12x2,f0=4,f'0=12 The objective…

Q: Find ƒ(x) if ƒ'(x) = 3x² - 4x + 4 and ƒ( − 1) – – 4. ƒ(x)

A: F

Q: 2 f(x) = 3x4 10

A:

Q: Q1/ Choose the correct answer: ( (1) The functions f. g and h are related by f(x) = g(x+1), g'(x) =…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: If f(2) =-3, g(2) =4, f' (2) =2- and g' (2) ==, then (2) - o' (2) =,

A:

Q: If f is one-to-one and f(1) = 5, f(3) = 7, and f(8) : - 10, find f-'(7), ƒ¯'(5), and f¯'(-10).

A: f is one to one and given  f(1)=5    therefore f-1(5)=1 f(3)=7    therefore f-1(7)=3 f(8)=-10…

Q: Find a function f(x) such that f'(x) = 9x² +2 and f(0) = 1 f(x) =

A:

Q: Let F(x) = f(x³) and G(x) = (f(x))5 . You also know that aª = 14, f(a) = 3, f'(a) = 13, f'(a³) = 14.…

A: Since we have the expression of F(x) and G(x) in terms of f(x), to find the derivative of both F(x)…

Q: let f(2)=3, f'(2)=4,g(2)=3,g'(3)=2. find (g o f)'(2)

A:

Q: Find f. f ''(t) = 9/ squareroot t,    f(4) = 31,    f '(4) = 12

A:

Q: X=(1)+ wam (xf pulf Z-x7=(x)₂ + £I-E#

A: Topic = Integration

Q: 2 9. If f(x) =-(x- 5), determine the following %3D 3 f(17)- f(8) а) 17-8 (12)- f (4) b) 12 - 4

A: The given function    f(x)=23x-5

Q: 1) If f(x) = x²(2), find f'(2)

A: f(x)=x2∫2xdtt2+5we know  d dx(∫axf(t)dt)=f(x)×d dx(x)-f(a)×d dx(a)

Q: 6. If f(2) = 3,f'(2) = 5, g(2) = –1, and g'(2) = –4, find (f g)'(2).

A:

Q: Let f (x) = x² 2 - 8 Find and simplify f'(x) and f" (x). + B where f'(x) = A = B = C = %3D Dx2 + E…

A:

Q: = (t² + 5t + 5) (5t² + 4), find ƒ'(t). If f(t) f’(t) = Find ƒʼ(3). ƒ'(3) =

A:

Q: For the function f(x) = (3x + 5)4, find f''(x), f''(0), f''(2), and f''(-3).

A:

Q: Suppose that f(-4)=3, f'(-4)=0, g(-4)=3, g'(-4) = 4. Use this to compute (f•g)'(-4)

A:

Q: r³ (x + 2) 6. Find f'(6) for f(x) = V (x + 3) Væ2 – 27 11 (a) 18 11 (b) 216 11

A: Some common derivative rules are, Also,

Q: 7. Determine f'(x) where

A: Derivative: - The rate of change of a function with respect to a variable is called derivative in…

Q: If ƒ(t) = (t² + 2t + 4) (7t² + 6), find ƒ´(t). Find f '(5).

A:

Q: Let F(x) = f(xf(x)) where f(2)=4, f(8)=5, f'(2)=-3, f'(8)=7. Find F'(2)

A:

Q: F(x) = 3Jx#6 + K Given find the value of k if f(-3) =19 f'-2) =- 3 ·

A:

Q: lo UcE - Uxx=0 4(x,0) = f(x) 4= (x2,0) = g(x)

A:

Q: f"(z) = 7z – 1 and f'(-2) =-1 and f(-2) = -4. Find f'(z) = and find f(4) = !!

A:

Q: Find f'(t) if f(t)= -2t² - 8t+7. f'(t) =

A: We need to find out the derivative of the given function.

Q: What conclusion can you draw if f' (c) = 0 and f'' (c) < 0?

A: Given: f' (c) = 0 and f'' (c) < 0