b. i. Suppose f is continous on [a, b] and differentiable on (a, b). Prove that if f(x) >0 for every x e(a, b) then f increases throughout (a, b) (4 marks) ii. Find the intervals on which f(x)=2+x-x2 increases and decreases. Hence, sketch the graph of this function. (4 marks)​

The weight of full–grown tomatoes at a farm is modeled by a normal distribution with a standard deviation of 18.4 grams. the 95 percent confidence interval for the mean weight of the tomatoes is calculated using a sample of 100 tomatoes. what is the margin of error (half the width of the confidence interval)?

For what values of x is x2 + 2x = 24 true?

Is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis.