The equation for the tangent line on the curve y=1+40x^3-3x^5 is y=120x^2-15x^4+1.
The slope of the tangent line at a specific point (x, y) on the curve y=1+40x^3-3x^5 is given by the derivative of the function at that point, which can be calculated using the power rule.
To find the equation of the tangent line on the curve y=1+40x^3-3x^5, you will need to determine the slope of the tangent line at a specific point and use the point-slope formula to write the equation of the line.
Yes, the power rule can be used to find the slope of the tangent line at any point on a curve that is in the form of y=x^n, where n is a constant.
Finding the tangent line on a curve can help determine the instantaneous rate of change of the curve at a specific point, which is useful in many applications such as optimization problems and motion analysis.