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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?On the graph of f(x)=sinx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?
- 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?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=10
- 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.Show that the function has partial derivative at the point (0,0) but is discontinuous at this point.Can you find the max value for y y'' + y = -sin(2x) if y(0) = 0 and y'(0) = 0