Volume Function Rate of Change

I. For the function $$f(x)=x^4$$, the derivative is $$f'(x)=4*x^3$$. II. Using the linearization formula $$f(x+\Delta x) \approx f(x)+f'(x)*\Delta x$$ with $$x=4$$ and $$\Delta x=-0.02$$ gives $$f(4-0.02) \approx 256+256*(-0.02)=250.88$$. III. The value $$250.88$$ is exactly equal to $$(3.98)^4$$. Which of the above statements is/are true?

Chain Rule At A Point

Variables in Related Rates Problems

The piecewise function shown above is defined as $$f(x)=\begin{cases} 2*x+1 & x<1 \\ x+2 & x\geq1 \end{cases}$$. Determine the value of x at which this function is not differentiable.

Higher-Order Trigonometric Derivatives

Suppose $$f(x)=\frac{x}{x+1}$$ with inverse function $$g(x)$$. Use the derivative formula for an inverse function to compute $$g'(1/2)$$.

Derivative of Exponential and Logarithmic Functions

Derivative of an Inverse Tangent Function

Applying the Chain Rule

I. The slope of the secant line connecting the points at $$x=1$$ and $$x=3$$ is given by $$\frac{f(3)-f(1)}{3-1} = \frac{0-0}{2} = 0$$. II. For the function $$f(x)=x^2-4*x+3$$, applying the power rule gives $$f'(x)=2*x-4$$; hence, $$f'(1) = 2*1-4 = -2$$. III. The average rate of change of $$f(x)$$ over the interval $$[1,3]$$ is equal to $$f'(3)$$. Based on the graph and the calculations, which of the above statements are true?

Derivative of a Constant Function

Quotient Rule Differentiation

Derivative of a Combination of Functions

Average Rate of Change of a Function

Horizontal Asymptote of a Rational Function

Limit of a Rational Function

Horizontal Asymptote of a Rational Function

Limit of a Rational Function

Limit Of An Oscillating Function