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Limit Definition of Derivative and Tangent Lines

Home | Calculus 1 | Definition of the Derivative | Limit Definition of Derivative and Tangent Lines

Use the limit definition of the derivative to find all points on the graph of

f(x)=4x312x2+9xf(x) = 4x^3 - 12x^2 + 9x

where the tangent lines to the graph have slope zero.

Posted by Will Lynch a year ago

Related Problems

Find the derivative of the following function using the limit definition of derivative,

f(x)=8x+4f(x) = 8x + 4

Compute f(x)f'(x) using the limit definition of the derivative f(a)=limh0f(a+h)f(a)hf'(a) = \lim_{h \to 0} \frac{f(a+h) - f(a)}{h} for the following 1. f(x) = 3 2. f(x) = 3x-1 3. f(x) = x2+xx^2 + x 4. f(x) = (x)\sqrt(x) 5. f(x) = 1/x

Use the definition of derivatives to find the derivative of the following function,

f(x)=x1f(x) = \sqrt{x - 1}

Find the slope of the tangent line to

f(x)=xf(x) = \sqrt{x}

when x = 1