Home > Calculus > Identifying Stationary Points (Critical Points) for a Function

What is the maximum value that the graph of #z=10-12w-2w^2#?

Answer 1

maximum value: #color(green)(28)#

Given
#color(white)("XXX")z=10-12w-2w^2#

The vertex will occur at the point where
#color(white)("XXX")(dz)/(dw)=0#
and since the coefficient of #w^2# is negative, the vertex sill be a maximum

In this case #(dz)/(dw)= -12-4w#
so the maximum will occur when #w=-3#
and #z=10-12 * (-3) - 2 * (-3)^2#
#color(white)("XXX")=10+36-18#
#color(white)("XXX")=28#

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Answer 2

Emily Ammerman

To find the maximum value of the function z = 10 - 12w - 2w^2, you need to complete the square for the quadratic term -2w^2 - 12w.

First, rewrite the function in the form z = a(w - h)^2 + k.

Next, determine the values of h and k by completing the square.

Then, identify the value of k, which represents the maximum value of the function.

The maximum value occurs when w = h, and z = k.

After completing the square and simplifying, the maximum value of the function will be found.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.