Question

week 4a - section 2 1 definition of the derivative: p (1 point) results for this submission all of the answers are correct. let ( f(x) ) be the function ( 12x^2 - 9x + 4 ). then the quotient ( \frac{f(10 + h) - f(10)}{h} ) can be simplified to ( ah + b ) for: ( a = 12 ) ( checkmark ) and ( b = 231 ) ( checkmark ) note: you can earn partial credit on this problem. preview my answers submit answers your score was recorded. scores are sent to uo canvas every 24 hours. you have attempted this problem 5 times. you received a score of 100% for this attempt. your overall recorded score is 100%. you have unlimited attempts remaining.

Explanation:

Step1: Compute $f(10+h)$

$$\begin{align*} f(10+h)&=12(10+h)^2 -9(10+h)+4\\ &=12(100+20h+h^2)-90-9h+4\\ &=1200+240h+12h^2-90-9h+4\\ &=12h^2+231h+1114 \end{align*}$$

Step2: Compute $f(10)$

$$\begin{align*} f(10)&=12(10)^2-9(10)+4\\ &=1200-90+4\\ &=1114 \end{align*}$$

Step3: Calculate the quotient $\frac{f(10+h)-f(10)}{h}$

$$\begin{align*} \frac{f(10+h)-f(10)}{h}&=\frac{(12h^2+231h+1114)-1114}{h}\\ &=\frac{12h^2+231h}{h}\\ &=12h+231 \end{align*}$$

Answer:

$a=12$, $b=231$