How does one check if the tangent line to a curve is correct with out graphing technology.
For example, y = (2x^2 + 5)(x - 3)^2, when x = 2 the tangent line is y = -18x+49.
How do I know that this is true?
How does one check if the tangent line to a curve is correct with out graphing technology.
For example, y = (2x^2 + 5)(x - 3)^2, when x = 2 the tangent line is y = -18x+49.
How do I know that this is true?
When x=2 the tangent line will be a number rather than an equation.
The derivative is defined as the tangent line of a function at any given point so if you correctly take the derivative (here use the chain rule and product rule) you will have an equation for the tangent line.
Given your equation I seriously doubt the tangent is -18x+49 since your original function is 5th order so I'd expect a derivative of 4th order.