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Features of Graphs:

Features of Graphs: . Limit: the intended (y)value of the function. Exists if value is the same as x approaches from each direction. Gradient: increasing(+), decreasing (-) Concavity: concave up ( f’’x is +) or concave down ( f’’x is -) Turning points: gradient=0

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Features of Graphs:

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  1. Features of Graphs: • Limit: the intended (y)value of the function. Exists if value is the same as x approaches from each direction. • Gradient: increasing(+), decreasing (-) • Concavity: concave up (f’’x is +) or concave down (f’’x is -) • Turning points: gradient=0 • Min TP: f’’(x) is + at that point • Max TP: f’’(x) is – at that point • Point of inflection: max gradient: f’’(x)=0 • Continuous: can be drawn with a single pen-stroke (no jumps/holes) • Discontinuous: • fundamental (e.g. asymptotes) • Piecewise • Holes • Differentiable: gradient is defined at that point (no hole/sharp point) Ex. 5.8 p.79

  2. (i) For the function f (x) above, what x value has both f (x) = 0 and f '(x) = 0? • (ii) For the function f (x) above, find all the value(s) of x that meet the following conditions: • (1) f (x) is not continuous • (2) f (x) is continuous but not differentiable • (3) f ''(x) > 0 • (iii) For the function f (x) above, find the value(s) of a where limx->af(x)→ does not exist.

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