Question

Find the most general antiderivative of the function. (Check your answer by differentiation. Use C for the constant of the antiderivative. Remember to use absolute values where appropriate.)

f(x) = 45−5x, x>0 .

Answer 1

F(x) = 45*x - (5/2)*x^2 + C

Explanation:

Here we want to find the antiderivative of the function:

f(x) = 45 - 5*x

Remember the general rule that, for a given function:

g(x) = a*x^n

the antiderivative is:

G(x) = (a/(n + 1))*a*x^(n + 1) + C

where C is a constant.

Then for the case of f(x) we have:

F(x) = (45/1)*x^1 - (5/2)*x^2 + C

F(x) = 45*x - (5/2)*x^2 + C

Now if we derivate this, we get:

dF(x)/dx = 1*45*x^0 - 2*(5/2)*x

dF(x)/dx = 45 - 5*x