Answer: 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
