Graphs 8
2 marks · EasyThe graph of is shown below.
Estimate the gradient of the curve at the point where by drawing a tangent.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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2 (accept estimates between 1.8 and 2.2) (±0.2)
Also accept: estimated value between 1.8 and 2.2
Common mistakes: Reads y value at x=1 rather than gradient; Gives x value instead of gradient
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Marking points
M1 · 1 mark · M1: Correctly draws or describes a tangent to the graph at or makes an attempt to find the gradient at this point.
A1 · 1 mark · A1: Gives an estimate for the gradient at between 1.8 and 2.2.
Worked solution
To estimate the gradient, draw a tangent at and find its slope:. Example: If your tangent passes through (0, -1) and (2, 3), then gradient = (3-(-1))/(2-0) = 4/2 = 2.