Over which interval is the graph of f(x) = βx2 + 3x + 8 increasing?
Accepted Solution
A:
Hello there!
To find the increasing intervals for this graph just based on the equation, we should find the turning points first.
Take the derivative of f(x)... f(x)=-xΒ²+3x+8 f'(x)=-2x+3
Set f'(x) equal to 0... 0=-2x+3 -3=-2x 3/2=x
This means that the x-value of our turning point is 3/2. Now we need to analyze the equation to figure out the end behavior of this graph as x approaches infinity and negative infinity. Since the leading coefficient is -1, as x approaches β, f(x) approaches -β Because the exponent of the leading term is even, the end behavior of f(x) as x approaches -β is also -β.
This means that the interval by which this parabola is increasing is... (-β,3/2)
PLEASE DON'T include 3/2 on the increasing interval because it's a turning point. The slope of the tangent line to the turning point is 0 so the graph isn't increasing OR decreasing at this point.