I have no idea how to do this, anyone have any hints?
Use linear approximation, i.e. the tangent line, to approximate as follows: cubed root 63.6
The equation of the tangent line to at f(x) x=64 can be written in the form y=
thanks
To approximate the cube root of 63.6 using linear approximation or the tangent line, you can follow these steps:
1. Start by finding the equation of the tangent line to the function at the point of interest, which in this case is x=64.
2. Recall that the equation of a tangent line can be written in the form y = mx + b, where m represents the slope of the line and b is the y-intercept.
3. To find the slope (m), you need to calculate the derivative of the function at x=64. The derivative represents the rate of change of the function at a particular point.
4. Once you have the slope, you can determine the y-intercept (b) of the tangent line by substituting the x and y coordinates of the point of interest (x=64, f(64)) into the equation y = mx + b.
5. Finally, write the equation of the tangent line in the form y = mx + b.
Let's work through the steps:
Step 1: Find the equation of the tangent line at x=64.
Step 2: Assume the equation of the tangent line is y = mx + b.
Step 3: Calculate the derivative of the function at x=64 to find the slope (m).
Step 4: Determine the y-intercept (b) by substituting the x and y coordinates of the point of interest into the equation y = mx + b.
Step 5: Write the equation of the tangent line by plugging in the calculated values of m and b into the form y = mx + b.
By following these steps, you can find the equation of the tangent line to approximate the cube root of 63.6 using linear approximation.