It costs Sugarco 25¢/lb to purchase the first 100 lb ofsugar, 20¢/lb to purchase the next 100 lb, and 15¢ to buyeach additional pound. Let f(x) be the cost of purchasing xpounds of sugar. Is f(x) continuous at all points? Are thereany points where f(x) has no derivative?

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Q: Q1) The dervative of the function f(x)= |x+2, using the definition of derivative is 1 b)- a) x+2 x+2

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Q: Find the value of the derivative (if it exists) at each indicated extremum

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Q: Find the derivatives of the functions in Exercis

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Q: Use the first derivatives test to find local exterma of f( x) =x3 -12x on R

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Q: 4. Consider the function f(x) = Vx – I (a) Use the limit definition of derivative to find f'(x)

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Q: -10 For f(x) = 2x-3 show that f'(x) = e using the limit definition of the derivative. ind the…

A: (a) f(x)=52x-3 f'(x)=limt→xf(t)-f(x)t-x        =limt→x52t-3-52x-3t-x…

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Q: Find the derivative by using the definition f(x + h) – f(x) f'(x) = lim where f(x) = v4x +7 h+0

A: given                  f(x)=4x+7

Q: In x se the second derivative test to find the local extrema for the function f (x) = x3 •

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Q: 6-Iff is a continuous at x=c, then f has a derivative at x=c. * a. True b. False

A: Consider the given statement "If f is a continuous at x = c, then f has a derivative at x = c".

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Q: Use the limit definition of the derivative to prove the following special case of the Quotient Rule:

A: We have to prove the following derivative by using limit definition: ddxfxx=x f'x-fxx2 We know for…

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A: Given that y=x+x2-8.

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Q: g(u) u +1

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Q: Let f(x) = x – 5x. Calculate the difference quotient f(2+h)-f(2) for h = -.1 If someone now told you…

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Q: Compute the derivative function f'(x) algebraically. f(x) = 8x – 5 %3D f'(x) =

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Q: 2. Given the graph of derivative f'(x), find: a) Any interval (s) where f(x) is decreasing b) Any…

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Q: 3- Show that this function is differentiable for all and find its derivative f(2) = f(x+jy) x - 15x…

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Q: Find the derivative of the function y(x) = n² +r". Assume that n is a positive y(x) = | constant.

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A: we have to determine the derivative of f(x) using definition  of derivative .f(x) is given as below

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Q: (0) x %3D 글*- St-3 5t – 3 2

A: Explanation of the answer is as follows

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Q: consider a continuous function y=f(x) whose first derivative is y'=x(x- 2).

A: We can find the interval as below.

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.