in problems 83 - 98, find the difference quotient of f; that is, find (f(x + h)-f(x))/h, h ≠ 0, for each…

in problems 83 - 98, find the difference quotient of f; that is, find (f(x + h)-f(x))/h, h ≠ 0, for each function. be sure to simplify. 83. f(x)=4x + 3 84. f(x)=-3x + 1 85. f(x)=x² - 4 86. f(x)=3x² + 2 87. f(x)=x² - x + 4 88. f(x)=3x² - 2x + 6 89. f(x)=5/(4x - 3) 90. f(x)=1/(x + 3) 91. f(x)=2x/(x + 3) 92. f(x)=5x/(x - 4) 93. f(x)=√(x - 2) 94. f(x)=√(x + 1)

in problems 83 - 98, find the difference quotient of f; that is, find (f(x + h)-f(x))/h, h ≠ 0, for each function. be sure to simplify. 83. f(x)=4x + 3 84. f(x)=-3x + 1 85. f(x)=x² - 4 86. f(x)=3x² + 2 87. f(x)=x² - x + 4 88. f(x)=3x² - 2x + 6 89. f(x)=5/(4x - 3) 90. f(x)=1/(x + 3) 91. f(x)=2x/(x + 3) 92. f(x)=5x/(x - 4) 93. f(x)=√(x - 2) 94. f(x)=√(x + 1)

Answer

Explanation:

Step1: Substitute $f(x)$ into difference - quotient formula

Given $f(x)=4x + 3$, then $f(x + h)=4(x + h)+3=4x+4h + 3$. The difference - quotient formula is $\frac{f(x + h)-f(x)}{h}$. Substitute the values: $\frac{(4x + 4h+3)-(4x + 3)}{h}$.

Step2: Simplify the numerator

$(4x + 4h+3)-(4x + 3)=4x+4h + 3-4x - 3=4h$.

Step3: Simplify the fraction

$\frac{4h}{h}=4$.

Answer:

$4$