Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. (Simplify your answers completely.)
f(x) = 2x^2 + 7x
http://www.cramster.com/answers-sep-10/calculus/step-process-find-step-process-find-slope-tangent_919293.aspx
To find the slope of the tangent line to the graph of the function f(x) = 2x^2 + 7x, we can use the four-step process. Here's how:
Step 1: Take the derivative of the function.
To find the derivative of the function f(x), we can use the power rule. The power rule states that the derivative of x^n is n*x^(n-1).
For f(x) = 2x^2 + 7x, we can apply the power rule to both terms separately:
f'(x) = (2 * 2x^(2-1)) + (7 * 1x^(1-1))
= 4x + 7
Step 2: Simplify the derivative.
The derivative of f(x) is 4x + 7.
Step 3: Substitute the x-coordinate of the given point into the derivative.
Let's say we want to find the slope of the tangent line at a specific point, (a, f(a)). To determine the slope, we substitute the x-coordinate (a) into the derivative we obtained in Step 2:
slope = 4a + 7
Step 4: Simplify the result if necessary.
The slope of the tangent line at any point on the graph of f(x) = 2x^2 + 7x is given by the expression 4a + 7, where 'a' is the x-coordinate of the point on the graph.
Note: It's important to remember that the slope of the tangent line changes at each point on the graph. To find the slope at a specific point, substitute the x-coordinate into the derivative.