2.3 Differentiabilityap Calculus

AP Calculus AB Differentiability and continuity. Posted by 3 years ago. Archived AP Calculus AB Differentiability and continuity. How to find constants. FREE-RESPONSE SOLUTIONS 2019 AB Question AB-2 (a) vtP is differentiable and therefore continuous on 0.3,2.8.Since 2.8 0.3 55 55 0 2.8 0.3 2.5 vvPP. All students take calculus All sin tan cos rule. Trigonometric ratios of some negative angles. Trigonometric ratios of 90 degree minus theta. Trigonometric ratios of 90 degree plus theta. Trigonometric ratios of 180 degree plus theta. Trigonometric ratios of 180 degree minus theta. Trigonometric ratios of 180 degree plus theta. Calculus Maximus Notes: 2.3 Differentiation Rules Page 3 of 7 The Sum and Difference & Konstant Rules The derivative of the sum of two functions f and g is the sum of the derivatives of f and g.

(1) Find the derivatives of the following functions using first principle.

(i) f(x) = 6Solution

(ii) f(x) = -4x + 7Solution

(iii) f(x) = -x2 + 2 Solution

(2) Find the derivatives from the left and from the right at x = 1 (if they exist) of the following functions. Are the functions differentiable at x = 1?

(i) f(x) = x - 1 Solution

(ii) f(x) = √(1 - x2) Solution

(3) Determine whether the following function is differentiable at the indicated values.

(i) f(x) = x x at x = 0 Solution

(ii) f(x) = x2 - 1 at x = 1 Solution

(iii) f(x) = x + x - 1 at x = 0, 1 Solution

(iv) f(x) = sin x at x = 0 Solution

(4) Show that the following functions are not differentiable at the indicated value of x.

(i)

Solution

(5) The graph of f is shown below. State with reasons that x values (the numbers), at which f is not differentiable.

Solution

(6) If f(x) = x + 100 + x2, test whether f'(-100) exists. (7) Examine the differentiability of functions in R by drawing the diagrams.

(i) sin x Solution

(ii) cos x Solution

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