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On what interval/s is the following function increasing? (Use interval notation. Round answers to 2 decimal places. Do not use the spacebar when typing your answer. If you need to use the infinity sign, just type "positive infinity" or "negative infinity".)

m(x)=4x^2-5x-7

(no multiple choice)

Verified Answer :

lukyo

There is a quadratic function

m(x) = 4x^2 - 5x - 7

whose coefficients are

a = 4, b = - 5, c = -7.

The graph of this function is a parabola, and as its quadratic coefficient is a = 4 > 0, then m has a minimum value that is marked as the vertex of the graph.

Now, just find the x-coordinate of the vertex point:

xv = - b/2a

xv = - (- 5)/(2 * 4)

xv = 5/8

xv = 0.625

xv = 0.63 (approximately)

Since m assumes its minimum value when x = 0.63, and the quadratic coefficient is positive, then m is increasing on the interval (0.63, + infinity).

I hope this helps. =)

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