Consider the function f(x)=2x^3−12x^2−30x+5 on the interval [−5,7]. Find the slope of the secant line (for this function) whose endpoints are (−5,f(−5)) and (7,f(7)). By the MVT, we know there exists a c in the open interval (−5,7) such that f′(c) is equal to slope of this secant line. Find the two values of c that work.
Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Consider the function f(x)=2x^3−12x^2−30x+5 on the interval [−5,7]. Find the slope of the secant line (for this function) whose endpoints are (−5,f(−5)) and (7,f(7)). By the MVT, we know there exists a c in the open interval (−5,7) such that f′(c) is equal to slope of this secant line. Find the two values of c that work.
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