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Produce graphs of $f$ that reveal all the importantaspects of the curve. In particular, you should use graphs of $f^{\prime}$and $f^{\prime \prime}$ to estimate the intervals of increase and decrease,extreme values, intervals of concavity, and inflection points.$$f(x)=4 x^{4}-32 x^{3}+89 x^{2}-95 x+29$$

the inflection points are $f(1.46)=-1.4017$ and $f(2.54)=3.99892$

Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 4

Curve Sketching

Derivatives

Differentiation

Applications of the Derivative

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So we want to produce graphs that reveal all the important aspects of the curve. And then we also want to use F prime and F double prime to estimate intervals of increase and decrease extreme values, intervals of con cavity and inflection points. So we're gonna have FFX Marigolds back to the 4th minus three X. Or my 30 to execute. That's 89 x squared And it's 95 back for 29. So we have our function here, we're going to want to have large values of Y. And we're gonna make our values back smaller, so maybe negative 100 200. So we get this as a function right here. And with this we see there's going to be these changes right here. This can be add inflection point. We see the function is going to be decreasing up until this point and then it will start increasing.

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