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Jaimee
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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.
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
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=3Part 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)