Question

Find the maximum value of the function f(x) = -0.7x2 – 2.7x + 4 to the nearest hundredth.

Answer 1

We need range

$\\ \sf\longmapsto f(x)=-0.7x^2-2.7x+4$

• See here x^2 will come greater than or equal to zero.

Least value of x^2 is 0

$\\ \sf\longmapsto -0.7(0)+2.7(0)+4=4$

So

range

$\\ \sf\longmapsto R_f=[4,\infty)$

Answer 2

Answer:

6.60

Step-by-step explanation:

Method I  - Algebra

For quadratics of the form ax^2 + b + c the vertex is at

x = -b/2a

x = 2.7/(2 * -0.7)

x = 2.7 / (-1.4)

x = -1.9285714286

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Method II - Calculus

Take the first derivative and set to zero

2(-0.7)x - 2.7 = 0

-1.4x - 2.7 = 0

-1.4x = 2.7

x = 2.7/(-1.4)

x = -1.9285714286

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pluging x = -1.9285714286 into the function

f(-1.9285714286) = -0.7(-1.9285714286)^2 - 2.7(-1.9285714286) + 4

f(-1.9285714286) = 6.6035714286

Rounded

f(-1.9285714286) = 6.60

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