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**1. Homework Statement**

The question states Use integral calculus to find the euation of the quartic that has (1,23) and (3, 15) and a y-intercept of 24.

**2. Homework Equations**

The previous part of the question was A quartic has stationary points of inflection at x=1 and x=3. Explain why f"(x)=k(x-1)(x-3) where k doesn't =0

**3. The Attempt at a Solution**

Part A:

A quartic has a non-stationary points of inflection at x=1 and x=3. Explain why f”(x)=k(x-1)(x-3) k≠0

A quartics points of inflection can be found by equating its second derivative to zero.

as f”(x)=k(x-1)(x-3) if f”(x)=0

0=k(x-1)(x-3)

if k≠0

0=(x-1)(x-3)

and hence x=1 and x=3

Part B:

Use integral calculus to find the equation of the quartic that has (1,23) and (3,15) and a y-intercept of 24.

f”(x)=k(x-1)(x-3)