Question

Find a function f(x) such that fʹ(x)=6 x⁵ and such that f(0)=10.

Answer 1

To find a function f(x) such that fʹ(x) = 6x⁵ and f(0) = 10, we integrate the derivative fʹ(x) to find the original function.

Step-by-step explanation:

To find a function f(x) such that fʹ(x) = 6x⁵ and f(0) = 10, we can integrate the derivative fʹ(x) to find the original function. The integral of 6x⁵ is (6/6)x⁶ = x⁶. Adding a constant of integration, C, we have f(x) = x⁶ + C. To find the value of C, we use the given condition f(0) = 10. Plugging in x = 0, we get 10 = 0⁶ + C, so C = 10. Therefore, the function f(x) = x⁶ + 10 satisfies the given conditions.