Question

(1 point) Find f if F"(x) = sin 2 + cos x, f(0) = 10, and f(0) = 7.

Answer 1

Answer:

F(x)=sin(2)*$x^{2}$-cos(x) +10x + 8

Step-by-step explanation:

in order to find F(x) you need to integrate two times.

-> First time

F'(x) = sin(2)*x + sin(x) + C,

if F'(0)=10 then F'(0)=sin(2)*(0) +sin(0) +c=10, so c=10.

Replacing C=10

F'(x) = sin(2)*x + sin(x) + 10.

-> Second time

F(x)=sin(2)*$x^{2}$-cos(x) +10x + $c_{2}$

if F(0) = 7 then sin(2)*0 - cos(0) + 10*0 +$c_{2}$=7

so $c_{2}$=8

Replacing this

F(x)=sin(2)*$x^{2}$-cos(x) +10x + 8

If f(0)=10 and f'(0)=7 the answer is F(x)=sin(2)*$x^{2}$-cos(x) +7x + 11

if F''(x)=sin(2x)+cos(x), f(0)=10, f'(0)=7 , the answer is F(x)=-sin(2x)/4 -cos(x) +15x/2+11