Infinite limit  cusp or vertical tangent a) Consider the function f(x) defined as follows f(x)...
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Infinite limit  cusp or vertical tangent a) Consider the function f(x) defined as follows f(x) = x { fx) = cuberoot(x) } Find the derivative f(x) by the power rule and show f(x) is not defined at x=0. [Note that this case where lim f(x) = +0 and lim f(x) = + o0 x+o+ x+0 corresponds to a vertical tangent line.] b) Consider the function g(x) defined as follows { gx) = cuberoot(x^2) Find the derivative g'(x) by the power rule and show g'(x) is not defined at x0. [Note that this case where lim g'(x) = +0 and lim g'(x) = x+ o+  00 x+0 corresponds to a cusp (which also has infinite slopeand a change in sign).] QUESTION 5 Evaluate derivative using power rule. a) f(x) = x12  9x7 + 4x5  4x4 + 3x? + 5 { f(x) = (2/3) x^12 9 x^7 + 4 x^5  4x^4 + 3x^2 + 5 } 3x6  2x + 5x³2x b) g(x) = { g(x) = [ (3x^6  2x^4 + 5x^3  2x) / (sqrt(x^5)) ] QUESTION 6 Equation of tangent line. Consider the following function f(x) f(x) = 2x3  3x?  2 { f(x) = 2x^3  3x^2  2 } %3D a) Evaluate f(3), the derivative of the function f(x) at x=3. b) Find equation of tangent line to the graph of f(x) at the point (3, f(3). Infinite limit  cusp or vertical tangent a) Consider the function f(x) defined as follows f(x) = x { fx) = cuberoot(x) } Find the derivative f(x) by the power rule and show f(x) is not defined at x=0. [Note that this case where lim f(x) = +0 and lim f(x) = + o0 x+o+ x+0 corresponds to a vertical tangent line.] b) Consider the function g(x) defined as follows { gx) = cuberoot(x^2) Find the derivative g'(x) by the power rule and show g'(x) is not defined at x0. [Note that this case where lim g'(x) = +0 and lim g'(x) = x+ o+  00 x+0 corresponds to a cusp (which also has infinite slopeand a change in sign).] QUESTION 5 Evaluate derivative using power rule. a) f(x) = x12  9x7 + 4x5  4x4 + 3x? + 5 { f(x) = (2/3) x^12 9 x^7 + 4 x^5  4x^4 + 3x^2 + 5 } 3x6  2x + 5x³2x b) g(x) = { g(x) = [ (3x^6  2x^4 + 5x^3  2x) / (sqrt(x^5)) ] QUESTION 6 Equation of tangent line. Consider the following function f(x) f(x) = 2x3  3x?  2 { f(x) = 2x^3  3x^2  2 } %3D a) Evaluate f(3), the derivative of the function f(x) at x=3. b) Find equation of tangent line to the graph of f(x) at the point (3, f(3).
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Related Book For
Calculus Early Transcendentals
ISBN: 9780321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
Posted Date:
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