What is the minimum or maximum of #f(x)=-2x^2+7x-3#?

Answer 1

What is the max or Min of #f(x) = - 2x^2 + 7x - 3#

Ans: Max at vertex (7/4, 1/16)

Since a < 0, the parabola opens downward, there is a max at the vertex. x-coordinate of vertex: #x = -b/(2a) = -7/-4 = 7/4# y-coordinate of vertex: #y = f(7/4) = - 49/16 + 49/4 - 3 = #

#= 49/16 - 48/16 = 1/16#

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Answer 2

Eva Abramson

To find the minimum or maximum of ( f(x) = -2x^2 + 7x - 3 ), you can use the formula for the vertex of a quadratic function, which is ( x = -\frac{b}{2a} ). Plugging in the coefficients ( a = -2 ) and ( b = 7 ) into the formula, we get ( x = -\frac{7}{2(-2)} = \frac{7}{4} ). To find the corresponding value of ( f(x) ), substitute ( x = \frac{7}{4} ) into the function: ( f\left(\frac{7}{4}\right) = -2\left(\frac{7}{4}\right)^2 + 7\left(\frac{7}{4}\right) - 3 ). Calculate this expression to find the maximum or minimum value.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.