5. Let f be a function continuous on R and F(x) = af f(t)dt. Then F"(0) is equal to 0 0 O f(0) ○ 2f(0) O f'(0)

Q: For which values of x is f ' (x) < 0?

A: Given,

Q: If y = f(x), then f'(x), y', [Select] dy da and f(x) all represent the of fat x.

A: If , then to determine the meaning of .

Q: Suppose that f (1) = 1, f'(2) = 5, f'(1) = 4, g(1) = 2, g'(1) = 7. Find a. (fo g)'(1) b. (9((x)))…

A:

Q: Use the table below to compute h'(-1) for h(x) = f(x) g(). (E) (), (1)6 () 1/2 -2 2 1 -3 1 2 1 4. -1…

A:

Q: f(x) = In(x)

A:

Q: 10. lim 1-0 e³1 - 1 t

A: We have to find the limit: limt→0e3t-1t

Q: If h and f are functions and g defined by g(t) = f(t) · h(t), then what is g'(t)? f'(t)h'(t) +…

A: We have given that gt=ft·ht Differentiate the above function w.r.t 't' g't=ddtft·ht

Q: If f(x) is continuous on (-15,-5)such that, -10 SI5 f(x)dx=13 and/" f(x)dx =6 then find f(x)dx -10…

A:

Q: If some function f(x) has a relative extrema at the point (c, f(c)), then f'(c) = 0 True False

A: if we want to fine any fuction has relative extrema then

Q: 5 3. Let F(x) /t2 17 dt. Find F'(x)

A: Given:

Q: Let F(x) = S c²dc. Compute F'(t) = F(t).

A: The fundamental theorem of Calculus says: If F(x)=∫0xf(t) dt...(1) then  F'(x)=dFdx=ddx∫0xf(t)…

Q: Suppose the function f and its derivative ƒ' have values as given in the following table. f(x) f'(x)…

A:

Q: Is the function F (x) = L", e“ dt concave (concave down) or convex (concave up) for x<0?

A: To solve the following problem

Q: Let f(t) be a continuous function with f(0) 5 and f(4) = 3. Compute F'(2), where cx² F(x) = [" .…

A:

Q: Prove that if f'(z)=0 then f(z) is a constant.

A:

Q: F(x) = sin t dt, [0,1] 0. F(x)]

A: The following formula for Maclaurin's series expansion of sin x will be used: sin x=x-x33!+x55!-...…

Q: 8 f'(t) dt 24, what is the value of f(8)? If f(3) 12,f is continuous, and 3

A: Given,

Q: Suppose f is a function for which f'and f" exist. You are given that: S(0) = 1 S'(0) = 5 %3D %3D…

A: here we use the integration by parts see below the answer and calculation

Q: Let f(x) = sin? (x). Define F(x) | f(t) dt. What is F" -) ?

A:

Q: F:[- 2, 2]→ R, F(x) = (- 3Xf + 1) di

A: Given: Fx=∫-2x2t-3t2+1dt For finding derivative of given function, we will use fundamental theorem…

Q: 2 3 4 5 6 x) 5 6 3 2 9 (x) 4 -1 1 2 ompute -3 نه نه -2 2 7 3 O [ 5 f'(x) dx.

A: we will find the required.

Q: let p(x)=g(f(x)). use the given table to find p'4

A: p(x)=g[f(x)] diff. w. r. to x p'(x)=g'[f(x)] . f'(x)  ..................(1)

Q: Let f(x)= I Determine f'(x). sin² (³+1) dt, x= [1,1].

A: Given: f(x)=∫-xx2sin2(t3+1)dt

Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

A:

Q: 5. If S = 472 and dr dt 1 2 then find d.S dt when r = = 7.

A: Given:- S=4πr2 ,drdt=12

Q: d f(x) 3. Use the table to evaluate dx g(x) x=1 x = 3 x = 5 x = 7 x = 9 f(x) 3 1 9. 5 f'(x) 5 1 3…

A: Given the table:

Q: 16 f'(t) = 1 + t2' f(1) = 0

A:

Q: f' (t) =t+1/t³, t>0, ƒ(1)= 6

A: Explanation and solutions is given below.....

Q: f(x) = 5x - 5

A:

Q: Find f'(1) ir f (x) = In(x2 + 1).

A: We use chain rule

Q: Let f and g be functions differentiable on R. with Find f(x)|x=2= d g(2) = 2, 9(x)\x=2 = 4, de…

A:

Q: Let f(x) = ²³ d. Find the value of ƒ¹ (2) af(x) 0 24 4 -8 -4 -24 12 -12 8

A:

Q: 1(b)   Answer with "true or false". In addition, if the answer is wrong, correct the statement.…

A:

Q: Find f' and f" for the function. f(t) 92²2²-7 t f'(t) F"(t) = 18t + 7 انا 2 14 18+ + X X

A: Given: f(t)=9t2-7t