SOLUTION: a. {{{ 12x - 5x^2 }}} What is the maximum value of this expression? b. {{{ y = 4x^2 + x - 2 }}} For which values of y will x be positive? Please show working, thanks in

Question 985669: a.

What is the maximum value of this expression?
b.

For which values of y will x be positive?
Please show working, thanks in advance
Found 2 solutions by macston, Alan3354:
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
a.

Maximum occurs when first derivative=0
Set=0

= Maximum value when x=6/5.
.

=
ANSWER: Maximum value is 7.2.
.
Please limit to one question per post.

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
a.

What is the maximum value of this expression?
Without calculus:
f(x) = -5x^2 + 12x
The max is the vertex at x = -b/2a = -12/-10 = 1.2
f(1.2) = 14.4 - 7.2
= 7.2
======================
b.

For which values of y will x be positive?
Find where y = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=33 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.593070330817254, -0.843070330817254. Here's your graph:

================
x = 0 at those 2 points, x1 & x2
y is positive for x < x1 and x > x2

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