Determine, WITHOUT GRAPHING, whether the two given quadratic functions have a maximum value or a minimum value and then find the value.
NOTE: What exactly is meant by a max and min value here?
(1) f(x) = -2x^2 + 8x + 3
(2) f(x) = 4x^2 - 8x + 3
Determine, WITHOUT GRAPHING, whether the two given quadratic functions have a maximum value or a minimum value and then find the value.
NOTE: What exactly is meant by a max and min value here?
(1) f(x) = -2x^2 + 8x + 3
(2) f(x) = 4x^2 - 8x + 3
1.) f'(x) = -4x + 8
0 = -4x + 8;
Solve for x;
x = 2
Thus, the critical point is at x = 2, and that's either a min or a max.
-2(2)^2 + 8(2) + 3
-2*4 + 16 + 3
-8 + 16 + 3
8 + 3 = 11
And thus, it'll be at (2, 11).
We can check by seeing whether the second deriv is pos or neg, and thus determine concavity.
f''(x) = -4, and thus it is a max, since it's concave down.
Therefore, we have a maximum at (2, 11).
Now, this question came from a precalculus chapter in my state exam prep book. Can you show me how to answer the question WITHOUT using calculus concepts?
I am not into calculus just yet. I am preparing for my state exam and calculus 1 and 2 are the last 4 chapters of my state study book.
Now, how do I answer such a question WITHOUT calculus?
Thanks!