#L, Çonsicder the graph ort the hnetion *-xー12 tex)= a) ind an equatidn Ot the secant line janing the rwo point (-2,-6) anel (4,0) Ose the mean value Theorem to determine Poirt c in the interrval (-2,4) such that b) a the tangent line at c the secant line Is parallel C) Aind tme equation of the taAngent line throuon ccites)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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#1. Consider the graph of the function \( f(x) = x^2 - x - 12 \).

a) Find an equation of the secant line joining the two points \((-2, -6)\) and \((4, 0)\).

b) Use the Mean Value Theorem to determine a point \( c \) in the interval \((-2, 4)\) such that the tangent line at \( c \) is parallel to the secant line.

c) Find the equation of the tangent line through \((c, f(c))\).
Transcribed Image Text:#1. Consider the graph of the function \( f(x) = x^2 - x - 12 \). a) Find an equation of the secant line joining the two points \((-2, -6)\) and \((4, 0)\). b) Use the Mean Value Theorem to determine a point \( c \) in the interval \((-2, 4)\) such that the tangent line at \( c \) is parallel to the secant line. c) Find the equation of the tangent line through \((c, f(c))\).
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