Question

The tangent line to the graph of y = h(x) at the point (-1, 6) passes through the point (4, 2). Find h(-1) and h'(-1).

How do I solve this?

Answer 1

• h(-1) = 6
• h'(-1) = -4/5

Explanation:

You want the values of h(-1) and h'(-1) given that the tangent to h(x) at (-1, 6) passes through (4, 2).

Point

A point on the graph of h(x) has the coordinates (x, h(x)). This means the point (-1, 6) tells you ...

x = -1

h(-1) = 6

Slope

The tangent line at point (-1, 6) will have a slope of h'(-1). We can find the slope of the tangent line using the slope formula:

m = (y2 -y1)/(x2 -x1)

m = (2 -6)/(4 -(-1)) = -4/5

The tells you ...

h'(-1) = -4/5

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Additional comment

The attachment shows one function h(x) that has this characteristic. There are infinitely many such functions.

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