Chapter 10.1, Problem 53E

(a)

To determine

To find the minimum value of function.

Answer to Problem 53E

0

Explanation of Solution

Given information: $f\left(x\right)=\sqrt{x}$

Formula Used: Square root function

Calculation:

  $f\left(x\right)=\sqrt{x}$

As the domain of square root function is greater than or equal to zero i.e. cannot be negative.

Graph cannot be negative. So,

Minimum value of function = 0

(b)

To determine

Does function have maximum value.

Answer to Problem 53E

No

Explanation of Solution

Given information: $f\left(x\right)=\sqrt{x}$

Formula Used: Square root function

Calculation:

  $f\left(x\right)=\sqrt{x}$

As the domain of square root function is greater than or equal to zero i.e. cannot be negative.

Graph cannot be negative. So,

No, it doesn’t have a maximum value.

(c)

To determine

Does function have maximum value and minimum value.

Answer to Problem 53E

Function $f(x)=-\sqrt{x}$

Maximum Value = 0

Doesn’t have Minimum Value.

Explanation of Solution

Given information: $f\left(x\right)=\sqrt{x}$

Formula Used: Square root function

Calculation:

Parent Function $f\left(x\right)=\sqrt{x}$

Function that has a maximum value,

  $f(x)=-\sqrt{x}$

As,

  $\sqrt{x}\ge 0$

Multiply by -1 both sides

  $-\sqrt{x}\ge -0$

So,

  $-\sqrt{x}\le 0$

Now, $f(x)=-\sqrt{x}$

  $f(x)\le 0$

Hence,

Range = $(-\infty ,0]$

Maximum Value = 0

Doesn’t have Minimum Value.

(d)

To determine

Square root function that has minimum value of -4.

Answer to Problem 53E

Function $f(x)=-4+\sqrt{x}$

Minimum Value = -4

Doesn’t have Maximum Value.

Explanation of Solution

Given information: $f\left(x\right)=\sqrt{x}$

Formula Used: Square root function

Calculation:

Parent Function $f\left(x\right)=\sqrt{x}$

Function that has a minimum value of -4,

  $f(x)=-4+\sqrt{x}$

As,

  $\sqrt{x}\ge 0$

Subtract by 4 both sides

  $-4+\sqrt{x}\ge -4$

Now, $f(x)=-4+\sqrt{x}$

  $f\left(x\right)\ge -4$

Hence,

Range = $[-4,\infty )$

Minimum Value = -4

Doesn’t have Maximum Value.