Estimate g(5.2)−g(5) if g′(5)=5.

1

Step-by-step explanation:

g'(5) = 5  the derivative of the function g(x) when x = 5 is 5, which is equal to the slope at that point.

Use a constant linear slope of 5 to estimate the difference between g(5.2) and g(5)

y2 - y1 = slope (x2 - x1)

here, you want to find the g(5.2) - g(5) which would be y2 - y1.

x2 = 5.2, x1 = 5, slope = 5

so plug in these values to find the difference

y2 - y1 = 5 * (5.2 - 5) = 5 * 0.2 = 1

answer: domain and range mean all possible values of x and y that could be substituted to the inequality. a solution means all possible values that make the inequality statement true. so while the range is still all real numbers, the solution is the shaded area, for which y will always be greater than the line of the function.