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The point P (4, –1) lies on the curve C with equation y = f( x ), x > 0, and f '(x) =x/2 - 6/√x + 3. Find the equation of the tangent to C at the point P , giving your answer in the form y = mx + c. Find f(x)

First step is to understand all the notation, i.e. the prime for derivative. We then need to understand that the derivative is the gradient of the tangent at a point. In this case at the point P we can find ...
LP
Answered by Leon P. • Maths tutor
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What is a sonata form?

A sonata form is a musical structure that originated from a ternary form (a three part form); coming into recognition in the early Classical era. Despite variations in the form, the general form consists of ...
IP
Answered by Isabella P. • Music tutor
7502 Views

Describe one form of minor extrusive activity and explain its formation.

Geysers are intermittent discharges of turbulent water from the Earth's surface. One of the most famous examples is Old Faithful in Yellowstone National Park, North America. There are several factors needed ...
AB
Answered by Amy B. • Geography tutor
3192 Views

Let g (x) = 2x sin x . (a) Find g′(x) . (b) Find the gradient of the graph of g at x = π .

a) f'(x)=uv'+vu' if f(x)= uv u=2x u'=2 v=sin(x) v'=cos(x) g'(x)=2x cos(x) +2sin(x) b) g'(π) = 2π cos(π)+2sin(π) = 2 π (-1) + 2 (0) g'(π) = -2π
MB
Answered by Matias B. • Maths tutor
10770 Views

Differentiate sin(x)cos(x) using the product rule.

The product rule states (assuming x' is the differential of x): (fg)​′​​=f​′​​g+fg​′​​ Substitute the values into the rule: (sin(x)cos(x))' = sin(x)'cos(x) + sin(x)cos(x)' (sin(x)cos(x))' = cos 2 (x) - sin 2...
MP
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