Question

Find f
F"(x)=8x^3+5. F(1)=0. F'(1)=8

Answer 1

F"(x)=8x^3+5.

F'(x) = int (8x^3+5) dx
F'(x) = (8x^4)/4+5x + C
F'(x) = 2x^4 + 5x + C

because of F'(1) = 8, then
F'(x) = 2x^4 + 5x + C
F'(1) = 2(1)^4 + 5(1) + C = 8
2(1)^4 + 5(1) + C = 8
2 + 5 + C = 8
C = 8-2-5
C = 8-7
C = 1

Answer 2

Thank you I get it now

Answer 3

So
F'(x) = 2x^4 + 5x + C
F'(x) = 2x^4 + 5x + 1

now, we'll find F(X)

F(x) = int (F'(x)) dx
F(x) = int ( 2x^4 + 5x + 1) dx
F(x) = (2x^5)/5 + (5x^2)/2 + x + C
F(x) = (2x^5)/5 + (5x^2)/2 + x + C

because of F(1) = 0, then
F(x) = (2x^5)/5 + (5x^2)/2 + x + C
F(1) = (2(1)^5)/5 + (5(1)^2)/2 + (1) + C = 0
(2(1)^5)/5 + (5(1)^2)/2 + (1) + C = 0
(2/5) + (5/2) + 1 + C = 0
C = (2/5) - (5/2) - 1
C = -3.1

So

F(x) = (2x^5)/5 + (5x^2)/2 + x + C
F(x) = (2x^5)/5 + (5x^2)/2 + x -3.1

Answer 4

you are welcome