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Definition : A function f ( x ) is called differentiable at x = a if f ′ ( x ) exists & f ( x ) is called differentiable onto an interval if the derivative present for each of the point in that interval.
The next theorem illustrates us a very nice relationship among functions which are continuous & those that are differentiable.
Theorem: If f ( x ) is differentiable at x = a then f ( x ) is continuous at the point x = a.
Note as well that this theorem does not work in reverse order . Assume f ( x ) = |x| and take a look at,
So,f ( x ) = xis continuous at x =0 to sketch the graph of a function.
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A number x is chosen at random from the numbers -3, -2, -1, 0 1, 2, 3. What is the probability that | x| Ans : x can take 7 values To get |x| Probability (| x |
2/4 + 3/4 =
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Classifying critical points : Let's classify critical points as relative maximums, relative minimums or neither minimums or maximums. Fermat's Theorem told us that all relative
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Differentiate following. f ( x ) = sin (3x 2 + x ) Solution It looks as the outside function is the sine & the inside function is 3x 2 +x. The derivative is then.
The two sides of a triangle are 17 cm and 28 cm long, and the length of the median drawn to the third side is equal to 19.5 cm. Find the distance from an endpoint of this median to
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