Question

the product of the minimum value of the function f(x) = 5|x| + 8 and the maximum value of the function g(x) = 12-|x+5| is

Answer 1

Answer:

Step-by-step explanation:(i)f(x)=∣x−2∣−1

Minimum value of ∣x−2∣=0

Minimum value of f(x)=minimum value of ∣x−2∣−1

=0−1=−1

Minimum value of f(x)=−1→(x=−2)

f(x) has no maximum value.

(ii)f(x)=−∣x+1∣+3

∣x+1∣>0

⇒−∣x+1∣<0

Maximum value of g(x)=maximum value of −∣x+1∣+3

=0+3=3

Maximum value of g(x)=3

There is no minimum value of g(x)

Answer 2

SOLUTION

TO DETERMINE

The product of the minimum value of the function f(x) = 5| x | + 8 and the maximum value of the function g(x) = 12 − | x + 5 |

EVALUATION

We know that minimum value of a modulus function is 0

Now for the function f(x) = 5| x | + 8

f(x) is minimum when | x | is minimum

So minimum value of f(x) = 0 + 8 = 8

Again for the function g(x) = 12 − | x + 5 |

g(x) is maximum when | x + 5 | is minimum

So maximum value of g(x) = 12 - 0 = 12

Hence the required product

= 8 × 12

= 96

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