Question

For $f(x) = \sqrt{5x + 11}$, find $f'(1)$ using the definition $f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$. Using this, find the tangent line to the graph of $y = \sqrt{5x + 11}$ at $x = 1$. Enter all values as integers, or fractions in lowest terms.

          For $f(x) = \sqrt{5x + 11}$, find $f'(1)$ using the definition $f'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h}$. Using this, find the tangent line to the graph of $y = \sqrt{5x + 11}$ at $x = 1$.

Enter all values as integers, or fractions in lowest terms.

$For f(x) = √(5x + 11), find f'(1) using the definition f'(a) = limh → 0(f(a+h) - f(a))/(h). Using this, find the tangent line to the graph of y = √(5x + 11) at x = 1. Enter all values as integers, or fractions in lowest terms.$

Added by Alexander T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

08/30/2023

Step 1

Step 1: Find f'(1) using the definition f'(a) = lim(h->0) (f(a+h) - f(a))/h f(x) = sqrt(5x + 11) f'(a) = lim(h->0) (f(a+h) - f(a))/h f'(1) = lim(h->0) (sqrt(5(1+h) + 11) - sqrt(5(1) + 11))/h f'(1) = lim(h->0) (sqrt(5+5h+11) - sqrt(16))/h f'(1) = lim(h->0) Show more…

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For f(x)=sqrt(5x+11), find f^(')(1) using the definition f^(')(a)=lim_(h->0)(f(a+h)-f(a))/(h). Using this, find the tangent line to the graph of y=sqrt(5x+11) at x=1. Enter all values as integers, or fractions in lowest terms. y= For f=5x+11,find f1using the definition fa=lim Enter all values as integers,or fractions in lowest terms h 12x-1+4