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Think About It In Exercises 53–56, sketch the graph of a function f having the given characteristics.
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Calculus (MindTap Course List)
- Use the definition of the derivative to find the equations of the lines described in Exercises 59–64. 59. The tangent line to f(x) = x² at x = -3. 60. The tangent line to f(x) = x² at x = 0. 61. The line tangent to the graph of y = 1 – x – x² at the point (1, –1). 62. The line tangent to the graph of y = 4x + 3 at the point (-2, –5). %3D 63. The line that passes through the point (3, 2) and is parallel to the tangent line to f(x) = - at x = -1. 64. The line that is perpendicular to the tangent line to f (x) = x4 +1 at x = 2 and also passes through the point (–1, 8). For each function f graphed in Exercises 65–68, determine the values of x at which f fails to be continuous and/or differen- tiable. At such points, determine any left or right continuity or differentiability. Sketch secant lines supporting your answers.arrow_forwardFind the point on the graph of the function y = 4 - x2 that is closest to the point (0,2)arrow_forwardDetermine whether the function is increasing, decreasing, or neither: I+ z* (d) g(t) = 13 +t (a) f(x)= 3¬* (b) f(x) = x2 + 1 (c) g(t) = t2 + tarrow_forward
- calculate the composite functions f o g and g o f, and determine their domains f(x)= 1/x^2+1 g(x)= x^-6 f(g(x))= g(f(x))=arrow_forwardSketch the graph of f if a = 2. (a) f(r) = a² (b) f(x) = -a (c) f(x) = 3a* (d) fx) = a**3 (e) f(x) = a* + 3 (f) f(x) = a-3 (g) f(x) = a – 3 (h) f(x) = a (1) fC) = (-) 6) flx) = a-arrow_forwardcompute f(x)-f(a)/x-a for the following function f(x)=x^2-3x+1arrow_forward
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