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(a) If the function $f(x)=x^{3}+a x^{2}+b x$ has the local minimum value $-\frac{2}{9} \sqrt{3}$ at $x=1 / \sqrt{3},$ what are the values of $a$ and $b ?$(b) Which of the tangent lines to the curve in part (a) has the smallest slope?

a. $a=0$$b=-1$b. at $x=0$

Calculus 1 / AB

Chapter 4

APPLICATIONS OF DIFFERENTIATION

Section 3

Derivatives and the Shapes of Graphs

Derivatives

Differentiation

Applications of the Derivative

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in this question, we have to determine the position in that. We know if Prime equals 23 X square past to a express, be so by the information the program have a prime off one over route off three course zero. That means our first equation will be to over Rudolph three. A. Pass me because to minus one, and we know if off one over route off three because two miners to over nine Route of three. That means we have root of 3/3 A plus B equals minus one so we can solve this system. The questions that we have a causes. They are the Pecos toe minus one. So this is for part eight and for property once we know and B F crime equals the three X Square miners. One. So when our attention a hustler smallest a slope LEM use F Prime Minister has lost terrorized a small with the value. So for this contracting function, the smallest of value were achieved at X equals 20 which means a prime of very close to minus one, so minus one is the smallest slope the 10 year lines can have

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