Question

If h''(t)=1, h'(2)=3 and h(4)=5, find h(6)

Answer 1

Do you know what the antiderivative of 1 is?

Answer 2

x

Answer 3

yes, but you have to add C as a constant of integration because both y = x and y = x + 2 have 1 as a derivative. So when you take the antiderivative of h"(t) = 1, you get

h'(t) = x + C

Then you use the fact that h'(2) = 3 to solve for C

Answer 4

so.. 2+C=3
then, solve for C

Answer 5

yes

Answer 6

C=1

Answer 7

right. so the first derivative is h'(t) = x + 1. now take the antiderivative of that

Answer 8

1/2x^2+x

Answer 9

h(t) = 1/2x^2+x+C
Use h(4)=5 to find C

Answer 10

C=-7

Answer 11

Right. h(t) = ½t² + t - 7. All that's left is to find h(6)

Answer 12

17

Answer 13

yes

Answer 14

thank you so much :)

Answer 15

you're welcome