Suppose that ƒ is a function given as f(x) = −x² + 5x − 3. Simplify the expression f(x + h). f(x+h) = x²- 2xh - h²+5x+5h-31 05 - Simplify the difference quotient, f(x + h) − f(x) - = h f(x + h) − f(x) - h
Suppose that ƒ is a function given as f(x) = −x² + 5x − 3. Simplify the expression f(x + h). f(x+h) = x²- 2xh - h²+5x+5h-31 05 - Simplify the difference quotient, f(x + h) − f(x) - = h f(x + h) − f(x) - h
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
Question
Transcribed Image Text:Suppose that f is a function given as f(x) = x² + 5x - 3.
Simplify the expression f(x + h).
f(x+h) = x².
-
2xh
h²
+5x+5h30
f(x + h) − f(x)
Simplify the difference quotient,
h
f(x + h) − f(x)
=
h
The derivative of the function at x is the limit of the difference quotient as h approaches zero.
f'(x) =lim
h→0
f(x + h) − f(x)
h
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