Theory question 103
IntegrationIf f″(x) = 2, f′(1) = 0 and f(0) = −8, find f(x).
Show the model answer
Model answer
f′(x) = 2x + k; f′(1) = 0 gives k = −2.
f(x) = x² − 2x + c; f(0) = −8 gives c = −8.
f(x) = x² − 2x − 8.
Explanation
Integrate twice, using one condition after each step.