Applications of Derivatives Final Exam Review

Front

What is the equation of the line tangent to f(x)= 4x^2+2x-1 at x=0?

Back

y=2x-1

Front

Find dy/dx by Implicit Differentiation for 2xy^3 - x^2y = 2

Back

dy/dx = \frac{2y(x-y^2)}{x(6y^2-x)}

Front

Find the slope of the tangent line at the given point x^3 +2xy -y^2=11 at (2,3)

Back

Slope = 9

Front

Water slowly evaporates from a circular shaped puddle. The area of the puddle decreases at a rate of 36π in²/hr. At what rate is the radius of the puddle changing when the radius is 5 in?

Back

Rate of change of radius = \frac{-\frac{18}{5} in}{hr}

Front

Find dy/dx by Implicit Differentiation for x^3 + y^3 = 36

Back

dy/dx = \frac{-x^2}{y^2}

Front

What is the definition of a derivative?

Back

The derivative of a function at a point is the slope of the tangent line to the graph of the function at that point.

Front

What is the product rule for differentiation?

Back

If u and v are functions of x, then \frac{d}{dx}(uv) = u'v + uv'.

Front

What is the quotient rule for differentiation?

Back

If u and v are functions of x, then \frac{d}{dx}(\frac{u}{v}) = \frac{u'v - uv'}{v^2}.

Front

What is implicit differentiation?

Back

Implicit differentiation is a technique used to find the derivative of a function defined implicitly by an equation involving both x and y.

Front

What is the chain rule for differentiation?

Back

If y = f(g(x)), then \frac{dy}{dx} = f'(g(x))g'(x).