Maths-
General
Easy
Question
The slope of the tangent to the curve
at
is
- 10
Hint:
We are given a curve. We have to find the tangent at the given point. To find the tangent, we will differentiate the equation w.r.t x.
The correct answer is: ![negative 3](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABcAAAANCAYAAABCZ/VdAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAIRJREFUeNpjYCAfOALxNiD+BsQ/gPgWEE8AYmEGKoD9QBwExGxIYgZAvIOBhuATrQxWAuIb1DZUHIgToeHuRS1D/6PhAmIVYsO4gCAQBwDxSSC2p1WY80AtoBn4QSuD9aCRSjE4CMShQMwCxEzQHHsfiOOpYbgtEG+BBsMPaI71YaAXAAC89SISy3j3xAAAAFN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bW8+LTwvbW8+PG1uPjM8L21uPjwvbWF0aD4G0J3oAAAAAElFTkSuQmCC)
The given curve is y = 6 + x + x2.
We have to find the slope tangent at point (2,4)
To find the slope we differentiate the curve w.r.t x.
![table attributes columnalign left end attributes row cell y equals 6 plus x minus x squared end cell row cell fraction numerator d y over denominator d x end fraction equals 0 plus 1 minus 2 x end cell end table](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIEAAAA/CAYAAADHYKtVAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAArbJhr3gAABFFJREFUeNrtnFFkHFEUQJ8VsaJKVVT1o6yKqqpSFRFVIaIqokJVRFWFfOxX/vpR0Y8q1Y+oqrIqoqpC1KqK/FRERFSJiqiq0q/KR36qqiJW2N5r7jCdvJmd2bz3Zua9e7jsvpFcc+fOe/e9vfcKweSBJkkDZB3kDJvEXUogVZDPbApmj03gNldBVl288csgCyB/6C14T8ZwjZMUE1Rcu/FJeug99P0oyDjImmN2wPtfJEdwinMgGwoiaxtmgCV6AXLDLMgtyfgUyCOFemogYwadYALksWT8IV1TTVJ96ABn8+aZd0CehMa6QL6DHI/Z58aJjG8Kpr+0MwFuv04Evt8Fea7Rlkn0JbWXUa5ToBbkAci0hq0QroV1kF3hHZZsUEygywmugczQ50GQZc22NK1PGfi2fwl87wb5AVJWrKdJbwo6XQcdlvTTjFON+Zt2Zp0gH2j3sRkxs2WpL1fsBj7PUDyg2lC4JTwlGb8Isq0xMJyiWeeCIVua1qeMNdqvVmgWKGnQsRTzfxuanABnmrfk2GMG7Ghan1JegYyAvAG5rUlHNWIXgpHyJw1OUKEzCQxyj1D8oXN6Nq1PyxSGW8UtjTo6hXdEOkExAdJLOgcVO0E3zTzBhzAM8lrTvZnWp4UbZOARzXrQWC9B/oLsk1Nc0eBs9Yj4Y54i+CLr0wY+/I+CcRqcyvrYDO5yXng/ZjAMwzAMwzAMwzAMwzAMw7QHJqGU2AzuggWUW2wGt8GfnefZDO6AGTLPQH4LL1sYU6cwhfoeXTdVs8BkBK75K8LLncfPWDGDqehNmg2QtDULTMGYDrzxQfAB+1k0pmoWmIz4SctBeHYIpqebqllgMgBrAWR18720RIS3iz6tahaYAjEq5JmymEs/FxozUbPAZLQNXJCMo2NMhsZM1CwwGYAR/ldaFpBLwstD3KZgMLwd1F2zwGQElljX6XwA09EHQH5Jgj5TNQsycNv6QngVTCg1obf5Qw/tfDY16vBL2bB2s0G6xvPuLFnWLCyHnG9Y6C0H95dDnT0FVin28ndm2OFlXeS8tjGrmoWbwjvNDPM0hcHafZimG0uczvNym2XNAk6ZQ5LxAbpmkxMIIe93aLoljzba7XeA8UmnZBzHdixzgj5aEmSYbsmTK/ZjrjUscoIyBb39EdeVtchpGhCTTrCneNZpxwlU6DoG8i5i2QtS2BY5hzXWTsRyULZkOaiQAyTpgl7YFjkqAkNZ7f+QBYEhdm/BPg5dKc4VCtki57CMkqHCzBV8i4hBHh7ZdyScLQrdIkcFKzQVdtDScF+k6xqeRydYFMk6nlrRIkcFGDjNUiCIP2nXxMEcCN3xi8kYKbgNzrRFDqebOw6nmzOcbu4ardLNEWvOrpmDJEk393H67NpmkqSb+xS2vTsTT5J08yCFP7tm/idNurmPs2fXtpIm3Rxx+uza5m1g0nRzPru2lKTp5nx2bTmt0s2tae/uGv8A82t7tnPa3nEAAAGgdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG10YWJsZSBjb2x1bW5hbGlnbj0ibGVmdCI+PG10cj48bXRkPjxtaT55PC9taT48bW8+PTwvbW8+PG1uPjY8L21uPjxtbz4rPC9tbz48bWk+eDwvbWk+PG1vPi08L21vPjxtc3VwPjxtaT54PC9taT48bW4+MjwvbW4+PC9tc3VwPjwvbXRkPjwvbXRyPjxtdHI+PG10ZD48bWZyYWM+PG1yb3c+PG1pPmQ8L21pPjxtaT55PC9taT48L21yb3c+PG1yb3c+PG1pPmQ8L21pPjxtaT54PC9taT48L21yb3c+PC9tZnJhYz48bW8+PTwvbW8+PG1uPjA8L21uPjxtbz4rPC9tbz48bW4+MTwvbW4+PG1vPi08L21vPjxtbj4yPC9tbj48bWk+eDwvbWk+PC9tdGQ+PC9tdHI+PC9tdGFibGU+PG1zcGFjZSBsaW5lYnJlYWs9Im5ld2xpbmUiLz48L21hdGg+ACe/KAAAAABJRU5ErkJggg==)
Slope m = ![open parentheses fraction numerator d y over denominator d x end fraction close parentheses subscript left parenthesis 2 comma 4 right parenthesis end subscript](data:image/png;base64,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)
m = (1 - 2 × 2)
= 1 - 4
= -3
The slope of the tangent at given point is -3.
To find the slope we differentiate the given curve w.r.t x.
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