(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

Posted by 3 years ago. Can someone help me with this question? (Ap Calc AB - Graphing/differentiability) Ap calculus. Differentiate any function with our calculus solver. Enter an expression and the variable to differentiate with respect to. Then click the Differentiate button. Solution to Example 1 a) For x = 0, the denominator of function f(x) is equal to 0 and f(x) is not defined and does not have a limit at x = 0.Therefore function f(x) is discontinuous at x = 0. AP Calculus Limits, Continuity, and Differentiability. 2,3 69, 3 xx fx xx.

(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? Anatomyreproductive system.

(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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(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.

Ottawa senators game used glovesottawa senators game used. (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

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

v4formath@gmail.com

We always appreciate your feedback.

2.3 Differentiabilityap Calculus Test

You can also visit the following web pages on different stuff in math.

WORD PROBLEMS

HCF and LCM word problems

Word problems on simple equations

Word problems on linear equations

Trigonometry word problems

2.3 Differentiabilityap Calculus Definition

Word problems on mixed fractrions

OTHER TOPICS

2.3 Differentiabilityap Calculus Notes

Ratio and proportion shortcuts

Converting repeating decimals in to fractions

SBI!