What is the maximum value of this function? f(x)=−16x²+32x+20

Using the vertex, it is found that the maximum value of the function is of 36.

The function is given by:

Which is a quadratic function with coefficients .

The maximum value of a quadratic function with is at the vertex, in which the value is:

Hence, in this problem:

The maximum value of the function is of 36.

A similar problem is given at link

The maximum value is 35.94

Step-by-step explanation:

We have the function:

f(x) = -16*x^2 + 34*x + 20

This is a quadratic equation, and the first thing we can see is that the leading coefficient is smaller than zero, which means that the "arms" of the graph will go downwards, which means that the maximum of our function will be at the vertex.

First, we know that the vertex of a quadratic function is when f'(x) = 0.

f'(x) = 2*(-16*x) + 34 = 0.

x = -34/(-2*16) = 34/32 = 17/16.

Now we evaluate our function in the point x = 17/16.

f(17/16) = -16*(17/16)^2 + 32*(17/16) + 20 = 35.94

The maximum value is 35.94