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- How are the absolute maximum and minimum similar to and different from the local extrema?What values of a and b make ƒ(x) = x3 + ax2 + bx have a local minimum at x = 4 and a point of inflection at x = 1?the value of x at which the FOC is satisfied give us the ........(maximum/minimum) of the function because the second derivative is ..........(positive/negative).
- Consider the function ƒ(x) = x3. Where is the critical pointof ƒ? Does ƒ have a local maximum or minimum at the critical point?On the graph of f(x)=sinx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?Explain how the First Derivative Test determines whetherƒ(x) = x2 has a local maximum or local minimum at the critical point x = 0.
- What value of a makes ƒ(x) = x2 + (a/x)have a local minimum at x = 2?If y is a function of x and the slope of the function is zero at x=10 then to determine that y reaches a minimum dy/dx must be ............... at x=10Show that the function has partial derivative at the point (0,0) but is discontinuous at this point.
- If the function tends to infinity at the endpoints of the interval, then the function must take on a minimum value at a critical point.Determine whether the following statement is true or false, and explain why. The cosine function has an infinite number of critical points where an absolute minimum occurs.How do I solve the derivative for x to find the critical points and identify the absolute minimum and maximum?