Question

F(x) = — 3х2 – 6х +5 maximum and minimum value

Answer 1

9514 1404 393

Answer:

  maximum: 8; no minimum

Step-by-step explanation:

A graph can be useful. I find a graphing calculator handy. It shows the maximum of the function is f(-1) = 8. Since the parabola goes to -∞ for large values of x, there is no minimum.

  maximum: 8

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You can also find the maximum by putting the function in vertex form.

  -3(x^2 +2x) +5 . . . . factor the leading coefficient from the x terms

 -3(x^2 +2x +1) +5 -(-3)(1) . . . . add the square of half the x-coefficient, subtract the equivalent amount

  -3(x +1)^2 +8 . . . . . . the vertex form of the expression for f(x)

This form is ...

  a(x -h)^2 +k . . . . . with a=-3, h=-1, k=8

so the vertex is (h, k) = (-1, 8) -- the same as shown on the graph. The negative value of 'a' tells you the parabola opens downward, so the vertex is the maximum. The maximum is 8 at x = -1.