Find all possible functions with the given derivative.

Question

1. If y′=x, then y = ____

2. If y′=x2, then y =____

3. If y′=x3, then y =____

Answer 1

Find all possible functions with the given derivative.

1. If y′ = x, then y = ____

2. If y′ = x², then y =____

3. If y′ = x³, then y =____

Detailed Solution:

1. If y′ = x, then y = ____ ==> If f ′ (x) = x, then f(x) = ∫ f ′ (x) dx ==> If f ′ (x) = x, then f(x) = ∫ x dx ==>

If f ′ (x) = x, then f(x) = x²/2 + C

2. If y′ = x², then y =____ ==> If f ′ (x) = x², then f(x) = ∫ f ′ (x) dx ==> If f ′ (x) = x², then f(x) = ∫ x² dx ==>

If f ′ (x) = x², then f(x) = x³/3 + K

3. If y′ = x³, then y =____ ==> If f ′ (x) = x³, then f(x) = ∫ f ′ (x) dx ==> If f ′ (x) = x³, then f(x) = ∫ x³ dx ==>

If f ′ (x) = x³, then f(x) = x⁴/4 + H