Deside?SwedishFred said:Homework Statement
Deside curve tangent in point x=-π/4
No.SwedishFred said:Homework Equations
f(x)=1/3sin(3x-π/4)
y=f(x)
The Attempt at a Solution
f`(-π/4)=-1
using the tangent equation
y=kx+m
y=-1*(-π/4)+m
y=1/3sin(3(-π/4)-π/4)
≈3.33*10^-14
SwedishFred said:3.33*10^-14=-1*(-π/4)+m
f(x)≈-1*(-π/4)+0,79
is this right ? I have a bad feeling...
To calculate the curve tangent at x=-π/4, you will need to use the first derivative of the function at that point. This can be found by taking the limit as h approaches 0 of [f(-π/4+h)-f(-π/4)]/h. Once you have the derivative, plug in x=-π/4 to get the slope of the curve at that point.
Calculating the curve tangent at x=-π/4 allows you to determine the slope or rate of change of the function at that specific point. This can be useful in analyzing the behavior of the function and making predictions about its future values.
A tangent line is a line that touches a curve at a single point, in this case x=-π/4. It represents the instantaneous rate of change of the function at that point. By calculating the curve tangent at x=-π/4, you are finding the slope of this tangent line.
If the function is not differentiable at x=-π/4, then the curve tangent cannot be calculated as the first derivative does not exist at that point. This could be due to a sharp turn or a cusp in the curve at that point.
Knowing the curve tangent at x=-π/4 can be applied in various fields such as physics, engineering, and economics. For example, in physics, it can be used to determine the velocity of a moving object at a specific point in time. In economics, it can be used to analyze the growth rate of a company's profits. Essentially, it can be used to understand the instantaneous rate of change of a phenomenon.