Question

1. f '(x) = 14x − 20x3; f(3) = 7

2. f ''(x) = x²,    f '(0) = 5,    f(0) = 3

3.

5/1+e^-5x dx

Answer 1

Integrating both side,

integration of kx^n is kx^{n+1}/{n+1}, where k is constant.

where is C is integral constant,

as given : f(3) = 7

Answer:

2>

integrating both side:

as f'(0) = C = 5

integrating it again :

as f(0) = C' = 3

Thus,

answer.

3>

= , by multiplying e^5x in numerator and denominator.

Substituting

the whole integration becomes:

where C is integral constant.

answer