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7. Consider the function f(x)={−(2x2−9)3x​ if x<−3 if x≥−3​ (i) By examining the left-hand derivative and the right-hand derivative for x=−3 determine if f is differentiable at x=−3 (See pp. 168-169(H).) (8) (ii) Is f continuous at x=−3 ? (Give a reason for your answer.) (iii) Is f continuously differentiable on (−∞,−3) ? Motivate. [12]
7. Consider the function f(x)={−(2x2−9)3x​ if x<−3 if x≥−3​ (i) By exaunining the left-hand derivative and the right-hand derivative for x=−3 determine if f in differentiable at x=−3 (See pp. 168-169(H).) (8) (ii) Is f continuous at x=−3 ? (Give a reason for your answer.) (iii) Is f continuously differentiable on (−∞,−3) ? Motivate. (2) |12]